E190 Captain reported a loss of aircraft control while taxiing after shutting down the right engine prior to APU generator being available for system 2 hydraulic power. Aircraft drifted approximately 20 feet from ramp center-line before Captain could regain braking and steering.

Narrative

Upon entering the ramp in ZZZ on line X; heading to gate XX; I called for shutdown of engine 2. First Officer questioned if I wanted to shut down 2 right now. I paused and confirmed the 2 minute cool down cycle had elapsed; and that we were taxiing straight with no use of the tiller. At this point I conformed I wanted to shutdown engine 2. I failed to note I had also called for the APU start in order to accommodate the delay in ground power at the gates in ZZZ; and that the APU hadn't completed its start cycle. Upon shutting down engine 2 as requested; system 2 went offline. The most significant result was a drift towards the empty center of the ramp area which caused a centerline deviation of maybe 20 feet before I was able to stop the airplane. By the time we were able to contact ramp; system 2 was back online and we were able to confirm full control and safely resume our taxi to the gate. After deplaning i did a complete shutdown of the airplane; and notified the incoming Captain of my failure; and the result.